Models of Generative Grammar

Smriti Singh

Generative Grammar

A Generative Grammar is a set of formal rules that can generate an infinite set of sentences that constitute the language as a whole.

Chomsky insisted that a grammar - Must systematically describe all of the sentences in a language

that a native speaker would regard as grammatical. Must sort out all of the possible "good" sentences from all of the

possible "bad" ones. Must use a finite set of rules. Must provide a way to account for our perceived ambiguity of

certain sentences.

Models of Generative Grammar

Several models of Generative Grammar have been formally investigated following Chomsky’s initial discussion of –

1. Finite State Grammars2. Phrase Structure Grammars and3. Transformational Grammars

Chomsky reviewed the two conceptions of grammar (1957): The simpler of the two, finite-state grammars, are the rule

systems that strung words together, one by one, and acknowledge no larger phrase structure.

More complex than finite-state grammars are grammars called phrase structure grammars that build up phrases out of words and put the phrases together into sentences.

Finite State Machine

Suppose we have a machine – That has a finite number of different internal

states -1. One of these states is an initial state and2. Another is a final state. That switches from one state to another by

producing a symbol. That begins in the initial state, runs through a

sequence of states and ends in the final state.

Finite State Machine (contd.)

Representing Grammar/machine that produces justthe two sentences – “the man comes” and “the

mancome”.

State Diagram

man comes

The

men come

Finite State Grammar

Each node in the diagram corresponds to a state. The sequence of words that has been produced is a

‘sentence’. Such machine defines a certain language; the set of

sentences that can be produced in this way. Language produced by such a machine is called a finite

state language. Machine that produces such a language is called a finite

state grammar. FSG is the simplest type of grammar which, with a finite

amount of apparatus, can generate an infinite number of sentences.

Properties of Finite State Grammars

Such grammars allow transition from one state to another.

Each state represents the grammatical restrictions that limit the choice of the next word.

We can have any number of closed loops of any length.

Machines that produce languages in this manner are also known as “finite state Markov processes”.

Problems with FSGs

As all languages are not finite state languages, it is impossible to produce all and only the grammatical sentences of a language.

There are processes that FSGs are not equipped to handle.

Context Free Grammar

In both linguistics and computer science, we are not merely interested in whether a string is grammatical or not, we want to know why it is grammatical.

CFG is a finite collection of rules which tells us that certain sentences/strings are grammatical and what their grammatical structure is.

A context free grammar is one in which all the rules apply regardless of the context i.e. they would be of the type ‘Rewrite X as Y’, no further conditions being specified.

An example of CFG

Here's a simple context free grammar for a small fragment of English:

S -> NP VPNP -> Det NVP -> V NPVP -> VDet -> aDet -> theN -> womanN -> manV -> shoots

Ingredients and properties of this

grammar What are the ingredients of this grammar?It contains three types of symbol:

1. ‘->’ = An instruction to rewrite whatever symbol appears to the left of the arrow as the symbol or string of symbols that appears to the right of the arrow.

2. Symbols written like: S, NP, VP, Det, N, V. These symbols are called non-terminal symbols. Each of these symbols is shorthand for a grammatical category.

3. Symbols in italics: a, the, woman, man, and shoots. A computer scientist would probably call these terminal symbols and linguists would probably call them lexical items.

Why Context Free?As only single non-terminals occur on the left side of the rules.

Rule explanation

This grammar contains nine rules. Each rule consists of a single non-terminal symbol, followed by

->, followed by a finite sequence made up of terminal and/or non-terminal symbols.

We interpret each rule X Y as the instruction “rewrite X as Y.” For example, rule (2) rewrites the symbol VP as the string of

symbols Verb + NP, and defines Verb + NP to be a construction of the type VP.

The symbol S (for "sentence") is designated as the initial symbol.

It is necessary to begin with a rule that has the initial symbol on the left.

Thereafter any rule may be applied in any order until no further rule is applicable.

Context Free Grammar (contd.)

Consider the string of words – a woman shoots a man. Is this grammatical according to our little grammar? And if it is, what structure does it have? The following tree answers both the questions:

Such a tree is called a parse tree, and it gives us two sorts of information:1. Information about strings 2. Information about structure

Problems with CFGs

A context free language is a language that can be generated by a context free grammar.

Some languages are context free, and some are not e.g. it seems plausible that English is a context free language.

Some dialects of Swiss-German are not context free. It can be proved mathematically that no context free

grammar can generate all (and only) the sentences that native speakers find acceptable and..

For such dialects, one needs to employ additional grammatical mechanisms, not merely context free rules.

Phrase Structure Grammar

It builds up phrases out of words and put the phrases together into sentences.

The kind of structural description assigned by a phrase-structure grammar is, in fact, an immediate constituent analysis of the sentence.

It assigns to each sentence that it generates a structural description.

It makes use of phrase structure rules.

Phrase Structure Grammar (contd.)

It enables us to express patterns of grammaticality. It provides a structural description to characterize the notion

of grammaticality. It provides a way to capture our intuitions about the

constituent structure of sentences It also provides a way to explain, or account for, our

perceived ambiguity of certain sentences e.g. “mistrust wounds”

S S NP VP VP NP

N V V N

Mistrust wounds Mistrust wounds

An example of a Phrase Structure Grammar

It generates and thereby defines as grammatical such sentences as "The man will hit the ball"

An example of a PSG (associated with constituent analysis) :

Derivation of a given sentence

Interpret each rule X Y as “rewrite X as Y.” Derive the sentence “the man hit the ball” using the given

grammar :

The numbers at the right of each line refer to the rule of the grammar used in constructing that line from the preceding line.

Representation using a Tree Diagram

The derivation of the last sentence using a Tree diagram : S NP VP

Det N Verb NP Det N

The man hit the ball Such a tree does not tell in what order the rules have been applied. Given a derivation of the sentence, its tree diagram can be constructed but

not vice versa. A tree diagram retains just what is essential in the derivation for determining

the constituent analysis. The sequence of words can be traced back to a single point of origin S

Inadequacies of PSG

Although Chomsky found phrase-structure grammar to be necessary, heargued that this was not sufficient.1. It under-generates i.e. fails to generate all the grammatical sentences

of the language e.g. He burst into a loud cry and left the room. The man was bitten by the dog. Did the dog bite the man? Was the man bitten by the dog?2. It over-generates. It blindly allows many sentences as grammatical

which are in fact ungrammatical e.g. *The boy died Bill. *The men would put the book.3. Not all cases of ambiguity are accounted for by such Grammar.4. To account for such phenomena, the grammar must also include special

transformational rules that grab phrases or pieces of phrases and move them around in specified ways.

References

Noam Chomsky. Syntactic Structures. The Hague: Mouton & Co., 1957

David Crystal. A Dictionary of Linguistics and Phonetics (Blackwell, 1984)

Noam Chomsky. Aspects of the Theory of Syntax (Cambridge, MA: MIT Press 1965)